According to [1]}, the trajectories generated by (HBS) assure fast minimization property of order \(\mathcal {O}\left(1/t^2\right)\)  for the decay \(g(x(t))-\min g,\)  provided \(\alpha \ge 3\) . For \(\alpha >3\) , it has been shown by Attouch-Chbani-Peypouquet-Redont [2]} that each trajectory generated by (HBS) converges weakly to a minimizer of the objective function \(g\) . Further, it is shown in [3]} and [4]} that the asymptotic convergence rate of the values is actually \(o(1/t^2)\) .
